From BR Bullpen
An appeal is an action through which the defending team requests that the umpire call out a member of the batting team for an action that has been completed.
Appeals are required for two situations: if a runner misses a base (including failing to touch home plate), or if a runner leaves his base early when advancing on a fly ball that has been caught. In both cases, the appeal takes place after completion of the play, and necessarily before the next pitch has been thrown. The defending team first indicates to the umpire that it wishes to make an appeal. The pitcher then steps off the mound and throws to a teammate at the base where the infraction occurred (i.e. the base that was missed, or the base from which the runner departed too soon). If the umpire agrees that the runner made the alleged mistake, he declares him out; if not, he makes the safe sign and play continues with the next pitch. Runs may be taken off the scoreboard as a result of a successful appeal.
Appeals are covered under section 7.10 of the rules.